Whenever I open a PDF from the internet, Acrobat X Pro asks me if I want to tag it. I never want to tag anything. Whether I create it from Word, from a scan, open it, whatever. Can someone tell me how to turn this tagging thing off?

It may be that you have an "accessibility" related application active.Something like a Windows Ease of Access application, Dragon Speak or something else.With any of these "active" (say as a background process) Adobe Reader / Acrobat will ask to prep the open PDF for proper use by the application.